Jessica T Mathews travels on a coach at the Bilderberg summit. She is on the steering committee of the summit and also on the advisory council of Transparency International USA. Photograph: Dan Kirby for the Guardian

Weaving down the alp came the Bilderbus, taking delegates on a whistlestop tour of the Tyrol. Buzzing along above it, at a crazy height, was its helicopter escort. I swear I could have bounced a euro off the roof of the coach and into the blades. If I’d wanted to have been dropped by an NSA sniper.

In the coach below it must have been like being in a washing machine. No wonder the delegates on board looked grumpy. Sitting up front, Jessica T Mathews had a face like thunder. Although maybe the cause of her headache wasn’t the helicopter, but rather the howling contradiction of being on the steering committee of the world’s most secretive policy summit and also on the advisory council of Transparency International USA.

Also on the bus was James Wolfensohn. A fellow member of TI-USA’s advisory council, Wolfensohn was the joint winner of their 2014 “integrity award”, an honour he shared with that other famous transparency campaigner, and the world’s fourth-biggest arms company, Raytheon. Previous winners of the integrity award include (and I kid you not) Coca-Cola, General Electric and the then secretary of state Hillary Rodham Clinton. The great email deleter herself. I think someone should tell TI-USA what “transparency” means. There may have been a mix-up somewhere down the line.

When it comes to transparency, this year’s Bilderberg summit fails in every way imaginable. Three prime ministers, two foreign ministers, one president, no press conference. No public oversight. Just a bunch of senior policymakers locked away for three days with some incredibly powerful corporate lobbyists, discussing subjects intimately related to public policy. Subjects such as “globalisation” and “current economic issues”, which in practical terms mean the giant trade deal, the Transatlantic Trade and Investment Partnership (TTIP).

Writhing around the issue of TTIP is an unholy knot of politicians and vested interests, their tails knotted together in the pitch black of an Austrian sewer. I’m going to put on some gloves, stick a clothes peg on my nose, and see if I can tease apart one corner of this filthy interconnected mass. Here goes.

First, I’ll pick a policymaker: how about Mikael Damberg? He’s the Swedish minister for enterprise and innovation, and 2015 is his first time round the table at Bilderberg. Sliding on to the chair next to him is Carola Lemne, the chief executive of the Confederation of Swedish Enterprise. This lobby group describes itself as “Sweden’s largest and most influential business federation”, and it’s extremely in favour of TTIP. As its website says: “Since 2007, the Confederation of Swedish Enterprise has worked actively to promote the success of these negotiations”.

Cosying up on the other side of Damberg is the chairman of Volvo, Swedish businessman Carl-Henric Svanberg. His company is a strong supporter of TTIP. Just last year, the official Twitter account of the Volvo Group tweeted: “A comprehensive ‪#TTIP agreement would reduce regulatory and trade barriers and boost US competitiveness.”

Damberg is trapped by Swedes. He slithers down under the table to try to make his escape. But there in the half-light he meets Swedish billionaire Jacob Wallenberg, the chairman of the industrial conglomerate Investor AB. Wallenberg was quoted by the US embassy in Sweden at the end of last year as saying: “‪TTIP is a once-in-a-lifetime opportunity. With a strong agreement consumers will be the beneficiaries.”

Lobbyist, company chairman, billionaire investor: a close-harmony chorus of influence pushing policy behind closed doors. And the chorus gets louder: Wallenberg and Svanberg, along with five fellow Bilderberg participants, are members of the influential European Round Table of Industrialists. And the ERT is a member of “the European Business Alliance for TTIP”. Layer upon layer of lobbying. And this is still just a fraction of the big business pro-TTIP influence at Bilderberg.

And all of it happening behind closed doors: out of sight of a disenchanted, disenfranchised electorate, 500 of whom gathered in the centre of Telfs on Saturday to protest against the way Bilderberg does business.

Protesters march in Telfs, Austria, against lobbying taking place at the Bilderberg summit. Photograph: Dan Kirby for the Guardian

“Public representants: let us know what’s going on,” implored one placard. “Stopps silents,” urged another. There was anger everywhere at the how elected politicians had tucked themselves away like this with big business. I spoke to Ursel Herbst, who had driven all the way from Cologne for this demonstration. “The way Bilderberg hide is stupid, like naughty children.” She smiled a tired smile. “I do not respect them.”

It’s ironic that the Bilderberg conference puts on such a show of power: taking over an alp for a “private meeting”, closing down the airspace, shutting roads, hovering helicopters over their buses ... and yet the net result is they come across as a bunch of naughty kids. They’ll just have to console themselves with exerting a huge influence on large swaths of transatlantic policy. It may not be much but it’s something.